Nonlocal ballistic and hydrodynamic transport in two-dimensional electron systems

Electrical transport in materials is typically diffusive, due to dominant momentum-relaxing scattering of carriers with the phonons or defects. In ultraclean material systems such as GaAs/AlGaAs or graphene/hBN heterostructures, momentum-relaxing can be suppressed, leading to the onset of non-diffusive transport regimes, where Ohm's law is no longer valid. Within these non-diffusive regimes, the hydrodynamic regime occurs when momentum-conserving electron-electron scattering length scale is smaller than the device length scale (usually at intermediate temperatures). On the other hand, weak electron-electron scattering (at low temperatures) results in ballistic transport, commonly understood using the familiar single-particle framework of injected carriers travelling in straight line trajectories with intermittent reflections off device boundaries. Both the ballistic and hydrodynamic regimes can exhibit a emph{negative} nonlocal resistance, and collective behaviour such as the formation of current vortices. In this work, we study nonlocal current-voltage characteristics in mesoscopic devices fabricated from a GaAs/AlGaAs heterostructure that hosts a two-dimensional electron system in a GaAs quantum well. First, we report a quadratic non-linearity in the nonlocal current-voltage characteristics that manifests in any device where a nonlocal voltage measurement is possible. Using measurements at low temperatures ($sim$ 4 K) across multiple devices and considering various contact configurations for each device, we show that the non-linearity is universal. We apply the non-linearity to rectification and frequency multiplication. We also report on a periodic peaks in the nonlocal voltage vs. magnetic field, in an enclosed mesoscopic geometry in which transverse magnetic focusing (TMF) is typically studied. These peaks occur at weak magnetic fields, are independent of the source-detector separation and are distinct from TMF. Our experimental findings are backed by an extensive set of simulations using in both the semiclassical as well as quantum-coherent transport models.